Null hypothesis and Alternative hypothesis examples

1. Although opinion polls have long found that about 40% of American adults say they attend religious services last week, this is almost certainly not true.
a. Why might we expect answers to a poll to overstate true church attendance?
b. You suspect strongly that the true percentage attending church in any given week is less than 40%. You plan to watch a random sample of adults and see whether or not they go to church. What are your null and alternative hypotheses?

2. The national unemployment rate in a recent month was 5.4%. You think the rate may be different in your city, so you plan to ask a sample of the city residents about their employment status. To see if the local rate differs significantly from 5.4% what hypothesis will you test?

3. A social scientist is studying the ages of executives in top management positions and thinks that the mean ages of technology executives is lower than that in other business sectors. What data need to be collected? What hypotheses are needed?

4. What null and alternative hypothesis should we use if we want to test the claim that on average children attending elementary schools in a certain metropolitan area are more than two miles from the school which they attend.

5. The manufacturer of a spot remover claims that his product removes 90 percent of all spots. In a random sample, the spot remover removes 11 of 16 stains. Write the null and alternative hypotheses.

6. In a study of the relationship between family size and intelligence, 49 "only children" had an IQ of 101.5 with a standard deviation of 6.7 and 50 "first born children" in two-child families had a mean IQ of 105.9 with a standard deviation of 5.8. Write out the relevant null and alternative hypothesis.